Underwater acoustic sensor localization using a broadband sound source in uniform linear motion

Acoustic sensors deployed on the sea floor can be localized using a broadband sound source travelling along a linear trajectory at a constant velocity and a constant depth below the sea surface. The absolute positions (X- and Y-coordinates) of the sensors are estimated in two steps, assuming that the XY-plane coincides with the (flat) sea surface. First, a local Cartesian x-y coordinate system is set up in such a way that, when the sensors and the moving source are projected onto the local xy-plane, its origin coincides with the projection of one of the sensors (called the reference sensor) and the x-axis is parallel to the projection of the source's linear trajectory which intersects the positive y-axis. The projection of the source trajectory onto the xy-plane is described by three motion parameters: the source speed together with the time and horizontal range at which the source is at the closest point of approach (CPA) to the reference sensor. The relative positions (x- and y-coordinates) of all other sensors, along with the three motion parameters, are estimated by measuring the temporal variation of the differential time-of-arrival (DTOA) of the signal emitted by the moving source at each pair of sensors and then minimizing the sum of the squared deviations of the noisy DTOA estimates from their predicted values over a sufficiently long period of time for all pairs of sensors. This relative position estimation assumes a priori knowledge of the source depth, the sensor depths and the side (either left or right) on which the source transits past the reference sensor. In the second step, the relative position estimate of each sensor is converted into an absolute position estimate by rotating the x- and y-axes by an angle equal to the source bearing at CPA, followed by a translational displacement determined by the absolute position of the reference sensor. The source bearing at CPA can be estimated if either the direction of travel of the source or the absolute position of another sensor is known. It can also be derived together with the absolute position of the reference sensor if the absolute position of the moving source is known as a function of time (e.g. from a GPS receiver attached to the source). The proposed sensor localization method is applied to real acoustic data recorded in a shallow water experiment where a small vessel travelled at a constant speed (at zero depth) past a wide-aperture linear horizontal array of eight hydrophones mounted 1 m above the sea bed. Assuming that the absolute positions of two of the sensors are known, the effectiveness of the method is verified by comparing the estimated absolute positions of the other six sensors with their nominal values.